Best place to put bug reports?
First, the most important thing to do is:

Make sure it's really a bug
We can only support the Blender binaries as have been distributed on
blender.org. First thing to test is therefore always if official
releases have the error. And if there's an error, test it with at
least one older official release to verify. This can reveal problems
with your graphics drivers for example, it's not likely that big
errors are there for many releases!
If the error is in current svn, try a build from someone else
(http://www.graphicall.org) or official test builds from (http://builder.blender.org) and when possible test it on another system.

The first thing users should do is try to consistently recreate the 'bug'. If you can repeat it, create a small and simplified test file (removing anything not needed to reproduce the bug) and submit it with a writeup of said bug.
Reports of &quot;random crashes&quot; or stuff that &quot;breaks at unspecified situations&quot; are unhelpful. Reporting them only creates noise and distraction rather than helping, if a developer can't reliably reproduce it he can't fix it.
If it is a graphical glitch, user interface corruption, viewport artifacts or any other issue related to graphics cards, the second step is updating your graphics cards to the latest available version. Make sure your GPU drivers are up to date, check the manufacturer site or the official brand site for newer versions. Many purported bugs in Blender are actually issues with the GPU that have recently been worked out in latest versions.
Likewise make sure there are no newly introduced known issues with the lastest drivers. Drivers themselves are also susceptible to bugs and some times newest versions introduce new issues. If you recently upgraded your hardware or installed updartes, rollback to last known good configuration and test if the issue is still there.
Reporting
The only place to report bugs is the bug tracker. Developers spend considerable time triaging new reports, avoid posting  duplicates. Browse through the already listed bugs in the tracker to see if someone else has already reported it. If not then you would want to create an account, sign in and click Submit New to file a new bug report. The submission form is very intuitive and lists some guidelines for submitting reports. A .blend file must be attached. Try to make the file as simple as possible (remove anything not strictly necessary to reproduce the issue) and clearly write the steps you took to discover the bug.
You can also quickly reach the bug tracker from inside Blender by going to the Help menu.

For very simple problems or things users are not sure about, before filing a report, users can always visit the #blendercoders channel on freenode.net via the webchat to voice their concerns and or request clarification or tips from the developers.
Additionally, here are some more bug reporting tips from a developer.

It may sound annoying to follow all these steps, but remember that if
you don’t, the developers waste time figuring it all out themselves or
trying to coax the information out of the user for each bug. Some
developers like Sergey, Campbell (ideasman42), and Brecht (brecht) handle a huge number of
bug reports; you can really help them out by filling good ones.

You can also watch on YouTube How to Report a Bug in 5 Steps